On June 10, 1854, Georg Friedrich Bernhard Riemann gave his classic lecture on curved space. [‘On This Day in Space’ Video ...

Bernhard Riemann was a man with a hypothesis. He was confident that it was true, probably. But he didn’t prove it. And attempts over the last century and a half by others to prove it have failed. A ...

The aim of this lectures is to provide an elementary introduction to the (orientable) Riemann surfaces. A tentative program is: Lect. 1: The sphere and projective transformations. Lect. 2: The torus ...

Sub-Riemannian geometry is a branch of differential geometry in which the motion of a system is constrained to lie within a specified distribution of allowable directions on a manifold. Unlike its ...